REDUCTION OF AN ACTIVATED SLUDGE PROCESS MODEL TO FACILITATE CONTROLLER TUNING M.J.M. Janssen1*, L.N. Hopkins1, B. Petersen1,2, P.A. Vanrolleghem1 1
BIOMATH Department, Ghent University, Coupure Links 653, B-9000 Gent, Belgium, *E-mail:
[email protected] 2 EPAS nv, Technologiepark 3, B-9052 Zwijnaarde, Belgium
KEYWORDS Activated sludge process, modelling, model reduction, controller tuning
SUMMARY The aim of this paper is to present a reduced model of an industrial activated sludge process which can be used for controller tuning. A reduced model was required because use of the full model is time consuming and computer intensive. The resulting model decreased simulation time by a factor of 3. Evaluation of the reduced model showed that it gives a good approximation of the full model, however, at intermediate influent concentrations of free ortho-phosphate the performance is lower. This did not significantly affect the controller tuning. Therefore, this simple model reduction is an effective tool for tuning the controller. INTRODUCTION The process under study is part of an industrial wastewater treatment plant (WWTP) with an average influent flow of 2700 m3/d. A characteristic of this WWTP is that the influent concentration of COD (Chemical Oxygen Demand) is extremely high (in the range of 1000 to 4000 g COD/m3, with peaks up to 9000 g COD/m3) and can vary dramatically over time because of the batch-wise production of different products in the industrial plant.
This study is confined to the activated sludge process with recycle as depicted in figure 1. The wastewater containing substrates and some biomass comes from the previous unit in the treatment plant and enters the activated sludge units (ASUs). In these units the substrates are converted aerobically by the biomass to more biomass, inert substances and CO2. The stream then continues to the clarifier, which separates the biomass from the effluent using gravity. Most solids are returned to the activated sludge units. Some of the settled biomass is wasted to maintain a solids residence time of 30 h on average. The wastewater contains a very high load of COD but is deficient in terms of phosphorus, that is, a lack of phosphorus is limiting the growth of the biomass. Phosphorus must be added to the system to increase the performance of the activated sludge units in terms of degradation of the COD in the wastewater and maintaining a stable biomass. A controller has been designed for the addition of the phosphorus (in the form of orthophosphate) using a model of the process. Modelling of such a system is not new and a variety of models exist for both the reactions occurring in the activated sludge units (Henze et al., 1987) and the settling (Takàcs et al., 1991; Otterpohl and Freund, 1992). These models are characterized by their complexity and highly non-linear nature. When these models are used for control purposes problems arise with respect to the time needed for tuning the controllers, since the optimized settings for the controller are found by performing
Figure 1: The flowscheme of the activated sludge system and the final clarifier (settler)
Figure 2: The unreduced model of the activated sludge process
multiple simulations. In the following section, first, a complete, unreduced model will be presented and, then, a solution to this problem, that is, a reduced model, will be presented. The reduced model is analyzed to determine its limitations and the effect of these limitations on controller tuning are discussed.
ASU1 and ASU3. Table 1: Fractions of the wastewater flow and the return sludge flow divided over the activated sludge units
wastewater recycle sludge
ASU1 0.36 0.35
ASU2 0.24 0.31
ASU3 0.40 0.34
THE UNREDUCED MODEL Modelling of the reactions The unreduced model of the process combines models of the hydraulics of the system, biological reactions in the activated sludge units and the separation process in the settler. The model was simulated with WEST. WEST is a distributed, multi-platform modelling and simulation environment designed for WWTPs. The units in the WWTP are represented by mass balances in the form of differential and algebraic equations which were solved using the Runge-Kutta 4-method with variable stepsize.* The hydraulic modelling The system consists of 3 parallel lanes flowing to the settler and one recycle flow. A tracer study was performed to determine the system hydraulics (Coen et al., 1998). Two of the lanes (ASU2 and ASU3) behave as two CSTRs (Continuous Stirred Tank Reactors) in series and the third (ASU1) as two lanes of two CSTRs in parallel. The recycle flow and the influent wastewater are not equally distributed over the three lanes. Table 1 lists the split fractions of the flows over the lanes. The wastewater is split up over the three units unevenly, while the recycle is split up evenly over the three lanes. This means that the units are unequally loaded: ASU2 has a significantly lower load than *
For more information on WEST see http://www.hemmis.be
The model describes carbon removal and accounts for the phosphorus deficiency in the system. It is a modified version of the IAWQ Model No.1 (Henze et al., 1987). This model is a complex, highly non-linear model due to the Monod-type expressions that it uses. It has 35 parameters and 15 states per tank. Most parameters are set at the default values (Henze et al., 1987) except for the yield of biomass growing on substrate (YH = 0.67), the maximum specific growth rate of the biomass (µmax = 0.408) and the decay rate of the biomass (bH = 0.312), which were determined using the methods given in Vanrolleghem et al. (1999). Settler modelling The final clarifier was modelled as a point settler, that is, as a separator with the split fraction of water determined by the recycle rate, which is 3000 m3/d and the solids split fraction (the fraction of settler influent solids that goes to the effluent) assumed to be 0.03. It is not a dynamic model. Model input As input for the model, files were constructed from data measured on-site combined with information retrieved from lab-scale experiments.
Figure 3: Reduced model of the activated sludge process
THE REDUCED MODEL The controller In order to decrease the calculation time, the model was reduced to a 2-tank configuration as can be seen in figure 3. The approximation was made that the wastewater and the recycle are evenly distributed over the 3 lanes, that is, that the three lanes behave in a similar way. For each of the activated sludge units the initial values of the derived state variables were summated as follows: all the initial values of the derived state variables in the first tanks in the three lanes were summated. The same was done with the second tanks in each of the lanes. The result of this method is that the total volume of the resulting two tanks in the reduced model is the same as the summation of the separate tanks in the unreduced model. The concentrations of the different species are the (weighted) average of the concentrations in the tanks of the unreduced model. The reduced model has 30 states. A dynamic simulation of 3 months now takes 1 minute to complete. When the controller is implemented, this takes 4.3 minutes. So the simulation time
A PI-controller was designed to dose phosphorus (75 %(m/m) phosphoric acid) to the system. The measured variable is the effluent concentration of phosphate and the manipulated variable is the flow of the phosphoric acid solution to the system. The aim of the controller is to maintain the effluent concentration of phosphate at a setpoint YS below a level which satisfies goverment restrictions. This ensures that sufficient phosphorus necessary for a healthy biomass is present in the system without endangering effluent quality. Summary The resulting model has 120 states. Simulation time of the unreduced model is 3.5 minutes for a dynamic simulation of 3 months. When the controller is implemented, this simulation time increases to 13.5 minutes due to the increased stiffness. A reduced model which is more time efficient will be described next. 0.035
6
0.03
5 SP [mg/l]
SP [g/m3]
0.025 0.02 0.015 0.01
3 2 1
0.005 0 125
4
145
165
185
0 125
205
150
t [d]
a.
unreduced model
175
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t [d] reduced model
unreduced model
b.
reduced model
20
SP [mg/l]
15 10 5 0 125
150
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t [d] unreduced model reduced model c. Figure 4: Effluent concentrations of SP calculated with the unreduced and the reduced model: a. SP,in = 1 mg/l; b. S = 10 mg/l; c. S = 20 mg/l
has reduced three-fold. The question now is, how good is the approximation? That is, does the reduced model still adequately describe the process? This will be discussed next.
1
SS_P
0.8
0.4
EVALUATION OF THE MODEL REDUCTION
0.2 0
The effect of the influent on the quality of the model reduction was evaluated using different constant influent concentrations for free orthophosphate (SP). This is illustrated in figure 4 for three different influent concentrations of SP (SP,in). There is an important observation with regard to the dynamic behaviour of the unreduced and the reduced models. The reduced model amplifies the dynamic behaviour of the system, that is, it has a greater standard deviation. There are two notable differences in the effluent concentration: • the difference in the range of the simulated effluent concentration; and • the sensitivity of the simulated effluent concentration to the type of model. The range of the simulated effluent concentration changes with different values for SP,in. If there is excess SP in the influent, the SP that has not been used will be present in the effluent. It is clear that the performance of the reduced model when compared with the unreduced model is dependent on the concentration of SP in the influent. This sensitivity to model reduction is plotted for different influent concentrations in figure 5, where the sensitivity is defined as:
SSP =
SP ,unreduced − SP ,reduced SP ,unreduced
0
The effect of the model reduction on controller tuning was examined both in the region of high sensitivity (intermediate SP,in) and low
20
20
15
15 10 5
150
175 t [d]
200
20
EFFECT OF MODEL REDUCTION ON CONTROLLER TUNING
SP [mg/l]
SP [mg/l]
15
phosphorus limited. This results in a low sensitivity; 2. At high concentrations none of the tanks in the two models are phosphorus limited (see figure 6a.). This also results in a low sensitivity; and 3. At intermediate concentrations some of the tanks are phosphorus limited and some are not. This results in a large value of the sensitivity. At intermediate concentrations the reduced model is phosphorus limited below 8 mg/l. However, in the unreduced model, due to an uneven distribution of wastewater across the three lanes (see Table 1), some tanks are in phosphorus limited conditions and some are not. This means that the reduced model is no longer a good approximation of the unreduced model. Figure 6a. illustrates this. Obviously, their average is different from the dynamics predicted by the reduced model which is not in phosphorus limiting conditions In conclusion, the reduced model is not a good approximation of phosphorus dynamics at intermediate SP,in. We now consider how this affects the controller.
t start ≤ t ≤ t end
5
10
Figure 5: Sensitivity to model reduction of the concentration of SP in the influent as a function of SP,in
(1)
10
5
SP,in [mg/l]
The variation in sensitivity to model reduction for changing SP,in is related to the behaviour of the system under two different conditions: Plimiting with low biomass growth and Psufficient with high biomass growth. This results in: 1. At low concentrations all of the tanks in the reduced and unreduced model are
0 125
0.6
0 125
150
175
200
t [d]
AS_3 AS_2 AS_1 AS_3 AS_2 AS_1 a. b. Figure 6: Effluent concentrations of SP from the three units for: a. SP,in = 20 mg/l; and b. SP,in = 10mg/l
sensitivity. The controller was tuned on the reduced model and its performance on the unreduced model was evaluated using the integral of squared errors (ISE) (see Table 2). Table 2: Values of the ISE for setpoint YS = 0.5 mg/l and YS = 7 mg/l in the unreduced and the reduced model
unreduced model reduced model
YS = 0.5 mg/l (high sensitivity) 1.07
YS = 7 mg/l (low sensitivity) 0.28
17.7
0.47
The performance of the reduced model operating in a region of high sensitivity is lower than in the region of low sensitivity. This result is intuitive. However, the ISE is very low in both regions for the unreduced model, so the unreduced model is suitable for tuning in both these regions. What may not be obvious is the reason why for both setpoints, the performance of the controller was better on the unreduced model when it was tuned on the reduced model. This is due to the dampening effect the unreduced model has on the dynamics. The controller requires less control action and hence results in less error. This means that whilst the reduced model is good for tuning, the controller should always be evaluated in the unreduced model to get a more accurate view of its performance. CONCLUSION This paper presented a reduced model of an industrial activated sludge process. This was done to increase calculation speed of the simulations for controller tuning. The resulting model reduced simulation time by a factor of 3. So controller tuning can be done more efficiently. The reduced model was validated by examining its sensitivity to the unreduced model. It was clear that at intermediate SP,in the performance of the model is not satisfactory. However, this did not affect the tuning of the controller. The reduced model can be used for tuning purposes over the whole range of SP,in. REFERENCES Coen F. et al., "Model-based characterisation of hydraulic, kinetic and influent properties of an industrial WWTP", Wat. Sci. Tech., 37(12), 317-326 (1998) Henze M. et al., "Activated Sludge Model No.1", IAWPRC Scientific and Technical Report No.1, IAWPRC, London, ISSN 1010-
707X (1987) Otterpohl R. and Freund M., "Dynamic models for clarifiers of activated sludge plants with dry and wet weather flows", Wat. Sci. Tech., 26(5-6), 1391-1400 (1992) Takàcs I. et al., "A dynamic model of the clarification-thickening process", Wat. Res., 25(10), 1263-1271 (1991) Vanrolleghem P.A. et al., "Estimating (combinations of) Activated Sludge Model No.1 parameters and components by respirometry", Wat. Sci. Tech., 39(1), 195-214 (1999) BIOGRAPHY Matty Janssen was born on March 8, 1973 in Weert, The Netherlands. In June 1995 he obtained a Bc. in Chemical Engineering at the Polytechnic College in Eindhoven. After graduating from Wageningen Agricultural University as a Bioprocess Engineer (MSc.) in September 1998, he found his first job as a research assistent at the department of Applied Mathematics, Biometrics & Process Control at Ghent University. There he worked within a government funded project concerning model based control of an industrial WWTP.
